Petraeus comes to CentCom with the challenge of stemming the rising violence in Afghanistan.

Petraeus, 55, shook Dempsey's hand — the pair are from the same West Point class of 1974 — and offered a few quiet words as he took official responsibility for CentCom's area of responsibility.

That responsibility is one of the largest in the U.S. military: nearly two dozen countries, including oversight for the wars in Iraq and Afghanistan and other hot spots such as Pakistan.

Petraeus, who has served three tours in Iraq including one as commander of the 101st Airborne Division, is credited with policies helping curb violence in Iraq.

And expectations that he will do the same in Afghanistan could hardly be higher.

Defense Secretary Robert Gates praised Petraeus and Dempsey, who had been the acting Centcom commander for seven months after Adm. William Fallon was forced to resign.

Speaking of Petraeus, Gates said "history will regard him as one of our nation's great battle captains. He is the preeminent soldier, scholar, statesman of his generation. And he is precisely the man we need at this command. ... Now he will take aim at our adversaries in Afghanistan."

Petraeus, who had served as the overall ground commander in Iraq since early 2007, is expected to quickly travel back to CentCom's area of responsibility in the Middle East.